In computer aided geometric design and computer graphics, computing rational parametrizations of curves and surfaces is a widely investigated problem. This paper is about the rational parametrization problem of fat quadric surfaces, where a fat quadric surface is a family of quadric surfaces with a parameter varied in a closed interval. We propose the canonical form method to parametrize fat quadric surfaces. However, our method will lead to a bad phenomenon namely artificial discontinuity. Then we improve the canonical form method to repair artificial discontinuities. Examples are provided to illustrate the eectiveness and robustness of our methods.